Question Number 173005 by Mikenice last updated on 04/Jul/22 Commented by MJS_new last updated on 05/Jul/22 $$\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{above}\:\mathrm{functions} \\ $$$$\mathrm{is}\:\mathrm{continuous}\:\mathrm{but}\:\mathrm{you}\:\mathrm{want}\:\mathrm{to}\:\mathrm{solve}\:{this}?! \\ $$ Terms of Service Privacy…
Question Number 172996 by Mathspace last updated on 04/Jul/22 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{{n}} }{ln}^{\mathrm{2}} {xdx} \\ $$$$\left.\mathrm{1}\right){lim}\:{U}_{{n}} ? \\ $$$$\left.\mathrm{2}\right){equivalent}\:{of}\:{U}_{{n}} \left({n}\rightarrow\infty\right) \\ $$ Answered by…
Question Number 41913 by math khazana by abdo last updated on 15/Aug/18 $${let}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{x}}{\mathrm{1}+{acosx}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{f}\left({a}\right)\: \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{x}}{\mathrm{1}+\mathrm{2}{cosx}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{x}}{\mathrm{1}−\mathrm{2}{cosx}}{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}}…
Question Number 172953 by Mathspace last updated on 03/Jul/22 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{lnx}\:{dx} \\ $$ Answered by Ar Brandon last updated on 03/Jul/22 $$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}}…
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Question Number 172944 by flor last updated on 03/Jul/22 $$\int\int_{{d}} {dxdy}\:\:\:\:\:\:{x}={y}^{\mathrm{2}} −\mathrm{1}\:\:\:\:\:\:{x}=\mathrm{1}−{y} \\ $$$${D}=? \\ $$ Commented by kaivan.ahmadi last updated on 04/Jul/22 $${x}={y}^{\mathrm{2}} −\mathrm{1}\Rightarrow{y}^{\mathrm{2}}…
Question Number 41854 by math khazana by abdo last updated on 14/Aug/18 $$\left.\mathrm{1}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \right){dx} \\ $$$$\left.\mathrm{2}\right){then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\:\mathrm{1}−{x}^{\mathrm{5}} \right)\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty}…
Question Number 41851 by de best last updated on 13/Aug/18 Commented by math khazana by abdo last updated on 14/Aug/18 $${changement}\:{y}={atan}\left({t}\right)\:{give} \\ $$$$\int\:\:\:\frac{{dy}}{{a}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:=\frac{\mathrm{1}}{{a}^{\mathrm{2}}…
Question Number 41848 by maxmathsup by imad last updated on 13/Aug/18 $${let}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{dx}}{\mathrm{1}+{asinx}}\:\:\:{with}\:{a}\in{R} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}+{sinx}}\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}{sinx}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 41846 by maxmathsup by imad last updated on 13/Aug/18 $${find}\:\:\int\:\:\:\:\:\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:\:+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$ Answered by MJS last updated on 13/Aug/18 $$\int\frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…